Pre-distortion method for telecommunication system and transmitter for mobile terminal of MC-CDMA telecommunication system

ABSTRACT

The invention concerns a pre-distortion method for a telecommunication system comprising a base station and at least one user. Each symbol of said user is spread with a coding sequence over a plurality of carriers to produce a plurality of corresponding frequency components of a signal (S i (t)) to be transmitted over an uplink transmission channel to said base station. Each of said frequency components is weighted by a weighting coefficient (ω i (l)), said weighting coefficients being determined from the channel response coefficients (h i (l)) of the corresponding downlink transmission channel at the respective frequencies of said carriers and from a value of the noise variance (σ 2 ) affecting said carriers.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a method for uplinkpre-distortion for a Multi-Carrier Code Division Multiple Access(MC-CDMA) telecommunication system.

[0003] 2. Description of the Related Art

[0004] MC-CDMA has been receiving widespread interest for wirelessbroadband multimedia applications. Multi-Carrier Code Division MultipleAccess (MC-CDMA) combines OFDM (Orthogonal Frequency Division Multiplex)modulation and the CDMA multiple access technique. This multiple accesstechnique was proposed for the first time by N. Yee et al. in thearticle entitled “Multicarrier CDMA in indoor wireless radio networks”which appeared in Proceedings of PMIC'93, Vol. 1, pages 109-113, 1993.The developments of this technique were reviewed by S. Hara et al. inthe article entitled “Overview of Multicarrier CDMA” published in IEEECommunication Magazine, pages 126-133, December 1997.

[0005] Unlike DS-CDMA (Direct Spread Code Division Multiple Access), inwhich the signal of each user is multiplied in the time domain in orderto spread its frequency spectrum, the signature here multiplies thesignal in the frequency domain, each element of the signaturemultiplying the signal of a different sub-carrier.

[0006] In general, MC-CDMA combines the advantageous features of CDMAand OFDM, i.e. high spectral efficiency, multiple access capabilities,robustness in presence of frequency selective channels, highflexibility, narrow-band interference rejection, simple one-tapequalisation, etc.

[0007] More specifically, FIG. 1 illustrates the structure of an MC-CDMAtransmitter for a given user i. We consider here the uplink, i.e. wesuppose that the transmitter is located in the mobile terminal (denotedMT) of a user i. Let d_(i)(n) be the symbol to be transmitted from useri at time nT to the base station, where d_(i)(n) belongs to themodulation alphabet. The symbol d_(i)(n) is first multiplied at 110 bythe a spreading sequence (and a scrambling sequence which is hereomitted for the sake of clarity) denoted c_(i)(t). The spreadingsequence consists of N “chips”, each “chip” being of duration T_(c), thetotal duration of the spreading sequence corresponding to a symbolperiod T. Without loss of generality, we assume otherwise specified inthe following that a single spreading sequence is allocated to the user.In general, a user may be allocated one or a plurality of orthogonalspreading sequences (multi-code allocation) according to the data raterequired. In order to mitigate intra-cell interference, the spreadingallocated to different users are preferably chosen orthogonal.

[0008] The result of the multiplication of the symbol d_(i)(n),hereinafter simply denoted d_(i) by the elements of the spreadingsequence gives N symbols multiplexed in 120 over a subset of Nfrequencies of an OFDM multiplex. In general the number N of frequenciesof said subset is a sub-multiple of the number L of frequencies of theOFDM multiplex. We assume in the following that L=N and denotec_(i)(l)=c_(i)(lT_(c)), l=0, . . . ,L−1 the values of the spreadingsequence elements for user i. The block of symbols multiplexed in 120 isthen subjected to an inverse fast Fourier transformation (IFFT) in themodule 130. In order to prevent intersymbol interference, a guardinterval of length typically greater than the duration of the impulseresponse of the transmission channel, is added to the MC-CDMA symbol.This is achieved in practice by adding a prefix (denoted Δ) identical tothe end of the said symbol. After being serialised in the parallel toserial converter 140, the MC-CDMA symbols are converted into an analoguesignal which is then filtered and RF frequency up-converted (not shown)before being amplified in amplifier 150 and transmitted over the uplinktransmission channel. The MC-CDMA method can essentially be regarded asa spreading in the spectral domain (before IFFT) followed by an OFDMmodulation.

[0009] The signal S_(i)(t) at time t which is supplied to the amplifierbefore being transmitted over the reverse link transmission channel cantherefore be written, if we omit the prefix: $\begin{matrix}{{S_{i}(t)} = {{d_{i}{\sum\limits_{l = 0}^{L - 1}\quad {{c_{i}(l)}{\exp \left( {{j \cdot 2}\pi \quad f_{l}t} \right)}\quad {for}\quad {nT}}}} \leq t < {\left( {n + 1} \right)T}}} & (1)\end{matrix}$

[0010] where f_(l)=(l−L/2)/T, l=0, . . . ,L−1 are the frequencies of theOFDM multiplex. More precisely, it should be understood that thetransmitted signal is in fact Re(S_(i)(t)exp(j2πF₀t)) where Re(.) standsfor the real part and F₀ is the RF carrier frequency. In other words,S_(i)(t) is the complex envelope of the transmitted signal.

[0011] An MC-CDMA receiver for a given user i has been illustratedschematically in FIG. 2. Since we consider the uplink, the receiver islocated at the base station.

[0012] After baseband demodulation, the signal is sampled at the “chip”frequency and the samples belonging to the guard interval are eliminated(elimination not shown). The signal obtained can be written:$\begin{matrix}{{R(t)} = {{{\sum\limits_{i = 0}^{K - 1}{\sum\limits_{l = 0}^{L - 1}\quad {{h_{i}(l)} \cdot {c_{i}(l)} \cdot d_{i} \cdot {\exp \left( {{j \cdot 2}\pi \quad f_{l}t} \right)}}}} + {{b(t)}\quad {for}\quad {nT}}} \leq t < {\left( {n + 1} \right)T}}} & (2)\end{matrix}$

[0013] where t takes successive sampling time values, K is the number ofusers and h_(i)(l) represents the response of the channel of the user ito the frequency of the subcarrier l of the MC-CDMA symbol transmittedat time n.T and where b(t) is the received noise.

[0014] The samples obtained by sampling the demodulated signal at the“chip” frequency are serial to parallel converted in 210 beforeundergoing an FFT in the module 220. The samples in the frequencydomain, output from 220, are despread by the spreading sequence of useri. To do this, the samples of the frequency domain are multiplied by thecoefficients c_(i)*(l) (here in the multipliers 230 ₀, . . . , 230_(L−1)) and then added (in adder 240). The summation result is detectedin 250 for supplying an estimated symbol {circumflex over (d)}_(i).Although not represented, the detection may comprise an error correctiondecoding like a Viterbi or a turbo-decoding which are known as such.

[0015] Furthermore, in MC-CDMA as in DS-CDMA, equalisation can beperformed at the receiving side in order to compensate for thedispersive effects of the transmission channel. In MC-CDMA, the samplesin the frequency domain are respectively multiplied with equalisingcoefficients q_(i)(l), l=0, . . . ,L−1 (here in 230 ₀, . . . , 230_(L−1)). However, in MC-CDMA in contrast to DS-CDMA, there is no simpleequalisation method for an uplink channel because the estimation of anuplink channel appears very complex.

[0016] Indeed in MC-CDMA, this estimation must be performed beforedespreading, i.e. at the chip level, when the signal from the differentusers are still combined. In contrast, in DS-CDMA, this estimation isusually performed after despreading, i.e. at the symbol level, andtherefore separately for each user.

[0017] In order to overcome the problem of channel estimation, it hasbeen proposed to implement a pre-distortion at the transmitter side(i.e. in the mobile terminal, denoted MT), so that a simple demodulatorcould be used at the receiver side without needing to estimate thechannel. The basic idea underlying pre-distortion is to exploit thereciprocity of the transmission channels (in TDD), that is the downlinkchannel estimation performed for the downlink demodulation is used as anestimation of the uplink channel. This implies both TDD-operation (samefrequency band used for the uplink and downlink), and relatively low MTmobility, i.e. low Doppler frequency.

[0018] An MC-CDMA TDD-system with (downlink) pre-distortion has beendescribed e.g. in the article of D. G. Jeong et al. entitled “Effects ofchannel estimation error in MC-CDMA/TDD systems” published in VTC2000-Spring Tokyo, IEEE 51^(st, Vol.) 3, pages 1773-1777. Pre-distortionis simply effected by multiplying each frequency component of theMC-CDMA symbol to be transmitted by the inverse of the channel responsecoefficient at said frequency, i.e. h_(i) ⁻¹(l). However, contrary towhat is put forward in the above mentioned paper such downlinkpre-distortion is not possible since the base station (denoted BS)cannot send one common pre-distorted multi-user signal which would havebeen optimised for the different propagation downlink channels from thebase station to the mobile terminals (h_(i) ⁻¹(l) depends on i). Thisproblem does not exist for the uplink transmission channels and onecould think to apply this pre-distortion technique for the uplink.However, multiplying the frequency components by the coefficients h_(i)⁻¹(l) may lead to a very high transmitted power if the uplinktransmission channel exhibits deep fades (i.e. h₁(l) may be close tozero for some subcarriers l). This high transmitted power decreases inturn the battery autonomy and may significantly increase theinterference towards adjacent cells.

SUMMARY OF THE INVENTION

[0019] An object of the present invention is to design a simplepre-distortion technique for an uplink channel in an MC-CDMA systemwhich does not present the drawbacks set out above.

[0020] To this end, the invention is defined by the pre-distortionmethod claimed in claim 1 and a transmitter implementing suchpre-distortion method as claimed in claim 10. Advantageous embodimentsof the invention are defined in the dependent claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The characteristics of the invention will emerge from a readingof the following description given in relation to the accompanyingfigures, amongst which:

[0022]FIG. 1 depicts schematically the structure of an MC-CDMAtransmitter known from the state of the art;

[0023]FIG. 2 depicts schematically the structure of an MC-CDMA receiverknown from the state of the art;

[0024]FIG. 3 depicts schematically the structure of an MC-CDMAtransmitter according to the invention;

[0025]FIG. 4 depicts schematically the structure of an MC-CDMA receiverto be used with the MC-CDMA transmitter according to the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] The basic idea underlying the invention stems from the analogybetween the pre-distortion and the demodulation issues. In both cases,the channel selectivity destroys the orthogonality of the spreadingsequences and orthogonality must be restored without unduly increasingthe noise level (in the demodulation case), or without unduly increasingthe transmitting power (in the pre-distortion case).

[0027] We refer back to the context of an MC-CDMA TDD telecommunicationsystem and more specifically to a base station receiving complex symbolsfrom a plurality of active users i=0, . . . ,K−1. Let us denote, foruser i, d_(i) the (complex scalar) transmitted symbol, c_(i) the vectorof components c_(i)(l), h_(i) the channel response vector of componentsh_(i)(l), w_(i) a pre-distortion vector of pre-distortion coefficientsw_(i)(l) and ω_(i) the corresponding vector of weighting coefficientsω_(i)(l)=w_(i)*(l). In general, c_(i), h_(i) w_(i) and ω_(i) are vectorsof size N, where N is the spreading sequence length. As mentioned above,it is assumed that N=L, i.e. that the code sequence length is equal tothe number of carriers and that one active user uses only one codesequence. However, the results set out below can be extended to the casewhere the number of carriers is greater than the spreading length(typically a multiple thereof) and/or to multi-code transmission.

[0028] After FFT, the received signal can be expressed as (see equation2): $\begin{matrix}{y = {{{\sum\limits_{j = 0}^{K - 1}{d_{j}\left( {\omega_{j} \circ h_{j} \circ c_{j}} \right)}} + \eta} = {{\sum\limits_{j = 0}^{K - 1}{d_{j}\left( {w_{j}^{*} \circ h_{j} \circ c_{j}} \right)}} + \eta}}} & (3)\end{matrix}$

[0029] where η is a vector of AWGN components of variance σ² and where ·expresses the vector multiplication element by element, that is(x·y)_(k)=x_(k)·y_(k).

[0030] The determination of the uplink channel responses being verydifficult to achieve, the receiver of the base station simplydemodulates the received signal by despreading it with each codesequence. The estimation of the symbol transmitted by the i^(h) user canbe expressed as: $\begin{matrix}{{\hat{d}}_{i} = {{{\mu c}_{i}^{H}y} = {{\mu {\sum\limits_{j = 0}^{K - 1}{d_{j}{c_{i}^{H} \cdot \left( {w_{j}^{*} \circ h_{j} \circ c_{j}} \right)}}}} + {{\mu c}_{i}^{H}\eta}}}} & (4)\end{matrix}$

[0031] where μ is a normalisation coefficient which for examplerepresents the gain of the automatic gain control (AGC). As the codesequences are assumed to be normalised, η_(i)=c_(i) ^(H)η has a varianceequal to σ².

[0032] The expression (4) can be simplified by introducing a set ofvectors v_(ij) where:

v _(ij) =c _(i) *·h _(j) ·c _(j)   (5)

[0033] Since the code sequences are assumed normalised and of constantamplitude, it can be noted that $v_{ii} = {\frac{1}{N}{h_{i}.}}$

[0034] Therefore the estimation of symbol d_(i) can then be rewrittenas: $\begin{matrix}{{\hat{d}}_{i} = {{\mu {\sum\limits_{j}{\quad {d_{j}\left( {w_{j}^{H} \cdot v_{ij}} \right)}}}} + {\mu\eta}_{i}}} & (6)\end{matrix}$

[0035] The power used by the mobile terminal i for transmitting thesymbol d_(i) can be expressed as:

P _(i) =|w _(i)|² =w _(i) ^(H) ·w _(i)   (7)

[0036] The interference term MAI_(i) (due to the users j≠i) is equal to:$\begin{matrix}{{MAI}_{i} = {\mu {\sum\limits_{j \neq i}\quad {d_{j}\left( {w_{j}^{H} \cdot v_{ij}} \right)}}}} & (8)\end{matrix}$

[0037] whereas the useful term is equal to: $\begin{matrix}{{\overset{\sim}{d}}_{i} = {{\mu \quad d_{i}w_{i}^{H}v_{ii}} = {\frac{\mu}{N}d_{i}w_{i}^{H}h_{i}}}} & (9)\end{matrix}$

[0038] The purpose of the invention is to find the vector w_(i) ofpre-distortion coefficients which maximises the value of {tilde over(d)}_(i), while minimising the interference MAI_(i) and transmittedpower P_(i). According to the invention, it is proposed to minimise aglobal mean square error taking into account all the users under theconstraint of a fixed transmitted power for each user. The power controlloop between the mobile terminal of user i and the base station ensuresthat the product of the transmitted power by the channel attenuation ismaintained about a desired value which is the same for all the activeusers. Without loss of generality, we may equivalently suppose in thefollowing that the transmitted power is the same for all the users, e.g.equal to N (that is the average power of each carrier is chosen equalto 1) and that the channel attenuation is identical for all thechannels. Let us consider the cost function: $\begin{matrix}{J = {\sum\limits_{i}{E\left( {{\hat{d}}_{i} - d_{i}} \right)}^{2}}} & (10)\end{matrix}$

[0039] The problem of minimisation under constraint mentioned aboveamounts to finding the minimum of the Lagrange function: $\begin{matrix}{L = {{\sum\limits_{i}{E\left( {{\hat{d}}_{i} - d_{i}} \right)}^{2}} + {\sum\limits_{i}{\lambda_{i}\left( {{w_{i}^{H} \cdot w_{i}} - N} \right)}}}} & (11)\end{matrix}$

[0040] where the λ_(i) are the Lagrange scalar multipliers.

[0041] The error on the estimation {circumflex over (d)}_(i)-d_(i) canbe obtained from (6) and (8): $\begin{matrix}{{{\hat{d}}_{i} - d_{i}} = {{d_{i}\left( {{{\mu w}_{i}^{H} \cdot v_{ii}} - 1} \right)} + {\mu {\sum\limits_{j \neq i}\quad {d_{j}\left( {w_{j}^{H} \cdot v_{ij}} \right)}}} + {\mu\eta}_{i}}} & (12)\end{matrix}$

[0042] The coefficient μ has to be optimised: for normalisedtransmission and channels, the amplitude of the useful part will dependon the pre-distortion method, and be equal to 1 only for w_(i)=h_(i). Abias will therefore be introduced, and must be compensated by AGC beforecalculation of the square error.

[0043] From (12), the global mean square error can be estimated:$\begin{matrix}{{E\left( {{\hat{d}}_{i} - d} \right)}^{2} = {{\mu^{2}w_{i}^{H}v_{ii}v_{ii}^{H}w_{i}} + 1 - {{\mu w}_{i}^{H}v_{ii}} - {{\mu v}_{ii}^{H}w_{i}} + {\mu^{2}{\sum\limits_{j \neq i}{w_{j}^{H}v_{ij}v_{ij}^{H}w_{j}}}} + {\mu^{2}\sigma^{2}}}} & (13) \\{{E\left( {{\hat{d}}_{i} - d} \right)}^{2} = {{\mu^{2}{\sum\limits_{j}{w_{j}^{H}v_{ij}v_{ij}^{H}w_{j}}}} + 1 - {{\mu w}_{i}^{H}v_{ii}} - {{\mu v}_{ii}^{H}w_{i}} + {\mu^{2}\sigma^{2}}}} & (14) \\{{~~~~~~~~~~~~~~~~~~~~}{L = {{\mu^{2}{\sum\limits_{i}{\sum\limits_{j}{w_{j}^{H}v_{ij}v_{ij}^{H}w_{j}}}}} + K - {\mu {\sum\limits_{i}{w_{i}^{H}v_{ii}}}} - {\mu {\sum\limits_{i}{v_{ii}^{H}w_{i}}}} + {K\quad \mu^{2}\sigma^{2}} + {\sum\limits_{i}{\lambda_{i}\left( {{w_{i}^{H}w_{i}} - N} \right)}}}}} & (15)\end{matrix}$

[0044] The first term of (15) can be rewritten as: $\begin{matrix}{{\sum\limits_{i}{\sum\limits_{j}{w_{j}^{H}v_{ij}v_{ij}^{H}w_{j}}}} = {{\sum\limits_{i}{\sum\limits_{j}{w_{i}^{H}v_{ji}v_{ji}^{H}w_{i}}}} = {{\sum\limits_{i}{{w_{i}^{H}\left( {\sum\limits_{j}{v_{ji}v_{ji}^{H}}} \right)}w_{i}}} = {\sum\limits_{i}{w_{i}^{H}\Phi_{i}w_{i}}}}}} & (16)\end{matrix}$

[0045] where the Hermitian matrix Φ_(i) is defined as: $\begin{matrix}{\Phi_{i} = {\sum\limits_{j}{v_{ji}v_{ji}^{H}}}} & (17)\end{matrix}$

[0046] Finally, the Lagrange function is expressed as: $\begin{matrix}{L = {{\mu^{2}{\sum\limits_{i}{w_{i}^{H}\Phi_{i}w_{i}}}} + K - {\mu {\sum\limits_{i}{w_{i}^{H}v_{ii}}}} - {\mu {\sum\limits_{i}{v_{ii}^{H}w_{i}}}} + {K\quad \mu^{2}\sigma^{2}} + {\sum\limits_{i}{\lambda_{i}\left( {{w_{i}^{H}w_{i}} - N} \right)}}}} & (18)\end{matrix}$

[0047] By calculating the gradients according to the vectorsw_(i)*=ω_(i) (the same result is obtained by calculating the gradientsaccording to vector w_(i)), the following set of equations is obtained:

∇_(w) _(i) ·L=μ ²Φ_(i) w _(i) −μv _(ii)+λ_(i) w _(i)=0 for 0≦i>K−1  (19)

[0048] By replacing v_(ii) with h_(i)/N: $\begin{matrix}{{\left( {{\mu^{2}\Phi_{i}} + {\lambda_{i}I}} \right)w_{i}} = {\frac{\mu}{N}h_{i}}} & (20)\end{matrix}$

[0049] where I is the identity matrix of size N×N.

[0050] At that stage, parameters λ_(i) and μ remain to be determined.Deriving L according to parameters μ provides a new equation:$\begin{matrix}{{{\partial L}/{\partial\mu}} = {{{2\mu {\sum\limits_{i}{w_{i}^{H}\Phi_{i}w_{i}}}} - {\sum\limits_{i}{w_{i}^{H}v_{ii}}} - {\sum\limits_{i}{v_{ii}^{H}w_{i}}} + {2K\quad {\mu\sigma}^{2}}} = 0}} & (21)\end{matrix}$

[0051] By combining equations (20) and (21), we obtain: $\begin{matrix}{{{2{\sum\limits_{i}{{w_{i}^{H}\left( {{\frac{1}{N}h_{i}} - {\frac{\lambda_{i}}{\mu}w_{i}}} \right)}\frac{1}{N}{\sum\limits_{i}{w_{i}^{H}h_{i}}}}}} - {\frac{1}{N}{\sum\limits_{i}{h_{i}^{H}w_{i}}}} + {2K\quad {\mu\sigma}^{2}}} = 0} & (22) \\{{{\frac{1}{N}{\sum\limits_{i}{w_{i}^{H}h_{i}}}} - {\frac{1}{N}{\sum\limits_{i}{h_{i}^{H}w_{i}}}} - {\frac{2}{\mu}{\sum\limits_{i}{\lambda_{i}{w_{i}}^{2}}}} + {2K\quad {\mu\sigma}^{2}}} = 0} & (23)\end{matrix}$

[0052] Furthermore, by multiplying on the left each term of equation(20) by w_(i) ^(H), we obtain: $\begin{matrix}{{{\mu^{2}w_{i}^{H}\Phi_{i}w_{i}} + {\lambda_{i}{w_{i}}^{2}}} = {\frac{\mu}{N}w_{i}^{H}h_{i}}} & (24)\end{matrix}$

[0053] As Φ_(i) is Hermitian, the left-hand term of (24) is real, andtherefore w_(i) ^(H)h_(i) is real and equal to h_(i) ^(H)w_(i). A simpleexpression between the λ_(t) and μ is obtained: $\begin{matrix}{{K\quad \mu^{2}\sigma^{2}} = {\sum\limits_{i}{\lambda_{i}{w_{i}}^{2}}}} & (25)\end{matrix}$

[0054] Since the transmitted power |w_(i)|² is assumed to be equal to N:$\begin{matrix}{{K\quad \mu^{2}\sigma^{2}} = {{\sum\limits_{i}\lambda_{i}} = {{NK}\overset{\_}{\lambda}}}} & (26)\end{matrix}$

[0055] where λ is the average value of the Lagrange multipliers λ_(i).The average value {overscore (λ)} can therefore be expressed as:$\begin{matrix}{\overset{\_}{\lambda} = \frac{\mu^{2}\sigma^{2}}{N}} & (27)\end{matrix}$

[0056] Let us recall that each Lagrange multiplier λ_(i) must be chosenso that each transmitted power |w_(i)|² is equal to N. It is verydifficult in practice to determine precisely the λ_(i) and μ values fromequations (20) and (25). According to the invention it is proposed toapproximate in equation (20) the λ_(i) values by the mean value{overscore (λ)}. Equation (20) then becomes: $\begin{matrix}{w_{i} = {{\frac{\mu}{N}\left( {{\mu^{2}\Phi_{i}} + {\overset{\_}{\lambda}I}} \right)^{- 1}h_{i}} = {{\frac{\mu}{N}\left( {{\mu^{2}\Phi_{i}} + {\frac{\mu^{2}\sigma^{2}}{N}I}} \right)^{- 1}h_{i}} = {\frac{1}{\mu \quad N}\left( {\Phi_{i} + {\frac{\sigma^{2}}{N}I}} \right)^{- 1}h_{i}}}}} & (28)\end{matrix}$

[0057] Due to the above approximation, equation (28) could provide asolution with a transmitted power slightly different from N. Inaddition, the transmitter does not know the value of parameter μ. Inpractice, the transmitter of user i solves the linear system ofequations (28) i.e. determines the unknown pre-distortion vector w_(i)and normalises the result so that |w_(i)|² is equal to N. Therefore,$\begin{matrix}{w_{i} = {{\alpha \left( {\Phi_{i} + {\frac{\sigma^{2}}{N}I}} \right)}^{- 1}h_{i}}} & (29)\end{matrix}$

[0058] where the real coefficient α corresponds to the normalisation ofw_(i).

[0059] Equivalently, instead of inverting the matrix$\Phi_{i} + {\frac{\sigma^{2}}{N}I}$

[0060] a system of N linear equations corresponding to${{\left( {\Phi_{i} + {\frac{\sigma^{2}}{N}I}} \right)w_{i}} = h_{i}},$

[0061] and where w_(i)(l) are the unknown coefficients, can be solved.The pre-distortion coefficients w_(i)(l) are then normalised as set outabove. The weighting coefficients are then obtained fromω_(i)(l)=w_(i)*(l).

[0062] Because of the presence of the matrix $\frac{\sigma^{2}}{N}I$

[0063] in expression (29) the pre-distortion coefficients w_(i)(l) arebounded even if a deep fade is experienced on the transmission channel.The value of the noise variance σ² is taken here as the inverse of theSINR (Signal to Interference plus Noise Ratio) for the demodulatedsignal. It can be estimated by the base station and transmitted to themobile terminal. Alternatively, a value of the noise variance σ² can beretrieved from a look-up table of typical values stored e.g. in a memoryof the mobile terminal. In general, the table is indexed by theparameters of the communication as the targeted BER level, the type ofmodulation, the type of channel coding used.

[0064] The matrix Φ_(i) for user i can be expressed as a function of thecode sequences c_(j) (for all the users j) and channel response h_(i) asfollows: $\begin{matrix}{\Phi_{i} = {{\sum\limits_{j}{v_{ji}v_{ji}^{H}}} = {\sum\limits_{j}{\left( {c_{j}^{*} \circ h_{i} \circ c_{i}} \right)\left( {c_{j}^{*} \circ h_{i} \circ c_{i}} \right)^{H}}}}} & (30) \\{\Phi_{i} = {\sum\limits_{j}{{{{Diag}\left( h_{i} \right)} \cdot {{Diag}\left( c_{i} \right)} \cdot \left( {c_{j}^{*}c_{j}^{T}} \right)}{{{Diag}\left( c_{i}^{*} \right)} \cdot {{Diag}\left( h_{i}^{*} \right)}}}}} & (31)\end{matrix}$

[0065] where .^(T) denotes the transpose operation and Diag(u) denotesthe diagonal matrix having the components of the vector u as diagonalelements. $\begin{matrix}{\Phi_{i} = {{{Diag}\left( h_{i} \right)} \cdot {{Diag}\left( c_{i} \right)} \cdot {\sum\limits_{j}{\left( {c_{j}^{*}c_{j}^{T}} \right) \cdot {{Diag}\left( c_{i}^{*} \right)} \cdot {{Diag}\left( h_{i}^{*} \right)}}}}} & (32)\end{matrix}$

[0066] and therefore:

Φ_(i) =Diag(h _(i))·Diag(c _(i))·C*C ^(T) ·Diag(c _(i)*)·Diag(h _(i)*)  (33)

[0067] where C is the N×K matrix of the code sequences.

[0068] As it can be seen from expression (33), the calculation of Φ_(i)merely entails a multiplication by diagonal matrices which requires fewsimple operations, and the calculation of the matrix C*C^(T) for whichfast algorithms, e.g. Fast Fourier Transform (FFT) or Walsh HadamardTransform (WHT) do exist. The latter matrix needs only to berecalculated when the number of users or the code allocation changes,for example every frame. It is important to note that the matrix Φ_(i)and hence the vector w_(i) does not depend on the vectors of channelcoefficients h_(j), j≠i. The transmitter of the mobile terminal i simplyneeds to know the codes of the active users and the coefficients of theuplink channel for user i. As indicated above, the coefficients of theuplink channel are supposed identical to those of the downlink channel.

[0069]FIG. 3 illustrates the structure of a MC-CDMA transmitterimplementing the uplink pre-distortion method according to theinvention. As in the prior art, the transmitter comprises a firstmultiplier 310 for multiplying the symbol to be transmitted by the codesequence of user i, a multiplexer 320 for multiplexing the results overthe OFDM multiplex, a module 330 performing an inverse Fourier transform(with prefix insertion), a parallel/serial converter 340 and anamplifier 350. In contrast with the prior art however, the transmitterfurther comprises a second multiplier 311 for multiplying the frequencycomponents d_(i)c_(i)(l) with the weighting coefficientsω_(i)(l)=w_(i)*(l) respectively. A channel estimation module 360estimates, e.g. from a received signal corresponding to a pilot symboltransmitted by the base station, the channel coefficients h_(i)(l). Fromthese coefficients and the knowledge of the code sequences allocated tothe K active users, the matrix Φ_(i) is calculated in module 361according to equation (33). From the matrix Φ_(i), the vector h_(i) anda value of noise variance σ² the module 362 determines thepre-distortion coefficients w_(i)(l) according to expression (29) andthen the weighting coefficients ω_(i)(l)=w_(i)*(l).

[0070] According to a first variant of the invention shown below, thecalculation of the matrix Φ_(i) in module 361 can be made in the realdomain. Indeed, if h_(i)(l)=ρ_(i)(l)e^(jθ) ^(_(i)) ^((l)) where ρ_(i)(l)and θ_(i)(l) are respectively the amplitude and the argument of thechannel response coefficient h_(i)(l), and we denote ρ_(i) and e^(jθ)^(_(i)) the vectors of components ρ_(i)(l) and e^(jθ) ^(_(i)) ^((l))respectively, we have:

Φ_(i) =Diag(e ^(jθ) ^(_(i)) )Φ_(i) Diag(e ^(−jθ) ^(_(i)) )   (34)

[0071] where we have denoted:

Φ_(i) =Diag(ρ_(i))·Diag(c _(i))·C*C ^(T) ·Diag(c _(i)*)·Diag(ρ _(i))  (35)

[0072] From equation (34) we obtain: $\begin{matrix}{w_{i} = {{\alpha \left( {{{{Diag}\left( ^{{j\theta}_{i}} \right)} \cdot \Phi_{i}^{\prime} \cdot {{Diag}\left( ^{- {j\theta}_{i}} \right)}} + {\frac{\sigma^{2}}{N}I}} \right)}^{- 1}h_{i}}} \\{w_{i} = {{\alpha \left( {{{Diag}\left( ^{{j\theta}_{i}} \right)} \cdot \left( {\Phi_{i}^{\prime} + {\frac{\sigma^{2}}{N}I}} \right) \cdot {{Diag}\left( ^{- {j\theta}_{i}} \right)}} \right)}^{- 1}h_{i}}} \\{w_{i} = {{{{\alpha Diag}\left( ^{{j\theta}_{i}} \right)} \cdot \left( {\Phi_{i}^{\prime} + {\frac{\sigma^{2}}{N}I}} \right)^{- 1} \cdot {{Diag}\left( ^{- {j\theta}_{i}} \right)}}h_{i}}} \\{w_{i} = {{{{\alpha Diag}\left( ^{{j\theta}_{i}} \right)} \cdot \left( {\Phi_{i}^{\prime} + {\frac{\sigma^{2}}{N}I}} \right)^{- 1}}\rho_{i}}}\end{matrix}$

[0073] Hence,

107 _(i) =Diag(e ^(−jθ) ^(_(i)) )ω_(i)   (36)

[0074] where$\omega_{i}^{\prime} = {{\alpha \cdot \left( {\Phi_{i}^{\prime} + {\frac{\sigma^{2}}{N}I}} \right)^{- 1}}{\rho_{i}.}}$

[0075] It is therefore possible to make the calculation in 361 and 362in the real domain and to apply last the phase factors e^(−jθ) ^(_(i))^((l)) to the real components ω_(i)(l).

[0076] A second variant of the invention is described hereafter. First,it is assumed that the MC-CDMA operates at full load and the codesequences are orthogonal or quasi-orthogonal. In such instance thematrix C*C^(T) is equal to the identity matrix and (33) then becomes:$\begin{matrix}{\Phi_{i} = {{{Diag}\left( {{h_{i}}^{2}{c_{i}}^{2}} \right)} = {\frac{1}{N}{{Diag}\left( {h_{i}}^{2} \right)}}}} & (37)\end{matrix}$

[0077] By replacing the expression (37) into (29), we obtain for thefull load case a pre-distortion vector of components w_(i)(l):$\begin{matrix}{{w_{i}(l)} = {\alpha \quad N\frac{h_{i}(l)}{{{h_{i}(l)}}^{2} + \sigma^{2}}}} & (38)\end{matrix}$

[0078] where α is a normalisation factor. In such instance, theweighting coefficients are expressed as: $\begin{matrix}{{\omega_{i}(l)} = {\alpha \quad N\frac{h_{i}^{*}(l)}{{{h_{i}(l)}}^{2} + \sigma^{2}}}} & (39)\end{matrix}$

[0079] When the system does not operate at full load, the matrix C*C^(T)is not equal to the identity matrix anymore but the diagonal termsremain predominant. Indeed, the diagonal terms are equal to:$\begin{matrix}{\gamma_{kk} = {{\sum\limits_{j = 0}^{K - 1}\quad {C_{kj}^{*}C_{kj}}} = \frac{K}{N}}} & (40)\end{matrix}$

[0080] and are expected to be larger than the off-diagonal terms$\gamma_{{kk}^{\prime}} = {\sum\limits_{j = 0}^{K - 1}\quad {C_{kj}^{*}C_{k^{\prime}j}}}$

[0081] since the terms C*_(kj)C_(k′j) tend to cancel out each other whenk≠k′. By approximating the matrix C*C^(T) to its diagonal terms, weobtain: $\begin{matrix}{{\Phi \approx {{Diag}\left( {\frac{K}{N}{h_{i}}^{2}{c_{i}}^{2}} \right)}} = {\frac{K}{N^{2}}{{Diag}\left( {h_{i}}^{2} \right)}}} & (41)\end{matrix}$

[0082] Finally, by replacing expression (41) into (29), the componentsof the pre-distortion vector, can be approximated as follows:$\begin{matrix}{{{w_{i}(l)} \approx {{\alpha \left\lbrack {{\frac{K}{N^{2}}{{h_{i}(l)}}^{2}} + \frac{\sigma^{2}}{N}} \right\rbrack}^{- 1}{h_{i}(l)}}} = {\alpha \frac{N^{2}}{K}\frac{h_{i}(l)}{{{h_{i}(l)}}^{2} + {\frac{N}{K}\sigma^{2}}}}} & (42)\end{matrix}$

[0083] where α is a normalisation factor. That is, the weightingcoefficients ω_(i)(l) are expressed as: $\begin{matrix}{{w_{i}(l)} = {\alpha \frac{N^{2}}{K}\frac{h_{i}^{*}(l)}{{{h_{i}(l)}}^{2} + {\frac{N}{K}\sigma^{2}}}}} & (43)\end{matrix}$

[0084] In addition, it can be shown that, if the channel responsecoefficients h_(i)(l), l=0, . . . ,L−1 are correlated, the MAI level isreduced and the following expression for the weighting coefficients isadvantageously used: $\begin{matrix}{{\omega_{i}(l)} = {\alpha \frac{N^{2}}{K}\frac{h_{i}^{*}(l)}{{\beta.{{h_{i}(l)}}^{2}} + {\frac{N}{K}\sigma^{2}}}}} & (44)\end{matrix}$

[0085] where β is a weighting factor, 0≦β≦1, which reflects thecorrelation of the channel response coefficients h_(i)(l), l=0, . . .,L−1 and departs from β=1 when the channel response coefficients arecorrelated.

[0086]FIG. 4 illustrates the structure of a MC-CDMA receiver in the basestation adapted to receive a signal transmitted by a MC-CDMA transmitteraccording to the invention. As in the prior art of FIG. 2, the presentreceiver comprises a serial to parallel converter 410, an FFT module 420(with prefix removal), multipliers 430 ₀ to 430 _(L−1) for multiplyingthe samples in the frequency domain by the conjugates c_(i)*(l) of theelements of the spreading sequence, an adder 440 and a detector 450 forsupplying the estimated symbols. As in the prior art, an error controldecoding can be provided, like a Viterbi decoding or a turbo-decoding.In contrast to the prior art, however, no equalisation is needed sincepre-distortion has been performed at the transmitter side.

[0087] Although the MC-CDMA transmitter illustrated in FIG. 3 has beendescribed in terms of functional modules e.g. computing or estimatingmeans, it goes without saying that all or part of this device can beimplemented by means of a single processor either dedicated forperforming all the functions depicted or in the form of a plurality ofprocessors either dedicated or programmed for each performing one orsome of said functions.

What is claimed is:
 1. Pre-distortion method for a telecommunicationsystem comprising a base station and at least one user (i), each symbol(d_(i)) of said user being spread with a coding sequence (c_(i)(l)) overa plurality of carriers (l) to produce a plurality of correspondingfrequency components (d_(i)c_(i)(l)) of a signal (S_(i)(t)) to betransmitted over an uplink transmission channel to said base station,characterised in that each of said frequency components is weighted by aweighting coefficient (ω_(i)(l)), said weighting coefficients being afunction of the channel response coefficients (h_(i)(l)) of thecorresponding downlink transmission channel at the frequencies (f_(l))of said carriers and of a value of the noise variance (σ²) affectingsaid carriers.
 2. Pre-distortion method according to claim 1,characterised in that, for said user (i), a vector ω_(i) representingsaid weighting coefficients is determined from a vector h_(i)representing said channel response coefficients as the conjugate of avector w_(i), the latter vector being obtained from an expression of thetype${w_{i} = {{\alpha \left( {\Phi_{i} + {\frac{\sigma^{2}}{N}I}} \right)}^{- 1}h_{i}}},$

where I is the identity matrix, σ² is said value of noise variance, N isthe length of said coding sequences, α is a normalisation factor, Φ_(i)is a matrix depending on the coding sequences allocated to the activeusers served by said base station and on said channel responsecoefficients.
 3. Pre-distortion method according to claim 2,characterised in that said matrix Φ_(i) is calculated according to anexpression of the typeΦ_(i)=Diag(h_(i))·Diag(c_(i))·C*C^(T)·Diag(c_(i)*)·Diag(h_(i)*) whereDiag(h_(i)) and Diag(h_(i)*) are diagonal matrices having respectivelysaid channel response coefficients and the conjugates thereof asdiagonal elements, Diag(c_(i)) and Diag(c_(i)*) are diagonal matriceshaving respectively the elements of the coding sequence of said user andthe conjugates thereof as diagonal elements, C is a matrix representingthe code sequences allocated to the active users, and where .* and .^(T)respectively denote the conjugate and the transpose operations. 4.Pre-distortion method according to claim 2, characterised in that saidmatrix Φ_(i) is calculated according to an expression of the type$\Phi_{i} = {\frac{K}{N^{2}}{{Diag}\left( \left| h_{i} \right|^{2} \right)}}$

where K is the number of active users and Diag(|h_(i)|²) is a diagonalmatrix having the square modulus of said channel response coefficientsas diagonal elements.
 5. Pre-distortion method according to claim 1,characterised in that said weighting coefficients ω_(i)(l) of thefrequency components relative to the carriers l are proportional to$\frac{h_{i}^{*}(l)}{\left. \beta \middle| {h_{i}(l)} \middle| {}_{2}{{+ \frac{N}{K}}\sigma^{2}} \right.}$

where h_(i)(l) is the channel response coefficient at the frequency ofcarrier l, N is the length of said code sequence and K is the number ofactive users served by said base station, β is a real weightingcoefficient and .* denotes the conjugate operation.
 6. Pre-distortionmethod according to claim 1, characterised in that for said user (i), avector ω′_(i) representing the respective amplitudes of said weightingcoefficients is determined from a vector ρ_(i) representing therespective amplitudes of said channel response coefficients, accordingto an expression of the type$\omega_{i}^{\prime} = {{\alpha \cdot \left( {\Phi_{i}^{\prime} + {\frac{\sigma^{2}}{N}I}} \right)^{- 1}}\rho_{i}}$

where I is the identity matrix, σ² is said value of noise variance, N isthe length of said code sequence, α is a normalisation factor and Φ_(i)is a matrix depending on the coding sequences allocated to the activeusers served by said base station and said channel responsecoefficients.
 7. Pre-distortion method according to claim 6,characterised in that said matrix Φ_(i) is calculated according to anexpression of the typeΦ_(i)=Diag(ρ_(i))·Diag(c_(i))·C*C^(T)·Diag(c_(i)*)·Diag(ρ_(i)) whereDiag(ρ_(i)) is a diagonal matrix having the components of said vectorρ_(i) as diagonal elements, Diag(c_(i)) and Diag(c_(i)*) are diagonalmatrices having respectively the elements of the coding sequence of saiduser and the conjugates thereof as diagonal elements, C is a matrixrepresenting the code sequences allocated to the active users, .* and.^(T) respectively denote the conjugate and the transpose operations. 8.Pre-distortion method according to claim 1, characterised in that saidvalue of noise variance is retrieved from a look-up table. 9.Pre-distortion method according to claim 1, characterised in that saidvalue of the noise variance is a measured value transmitted by said basestation.
 10. Transmitter for a mobile terminal of an MC-CDMAtelecommunication system comprising spreading means (310) for spreadinga symbol (d_(i)) to be transmitted over a plurality of carriers (l) toproduce a plurality of frequency components (d_(i)c_(i)(l)),characterised by estimating means (360) for estimating the channelresponse coefficients (h_(i)(l)) of the downlink transmission channel atthe frequencies (f_(l)) of said carriers, calculating means (361, 362)deriving from said channel response coefficients and a value of thenoise variance (σ²) affecting said carriers, a plurality of weightingcoefficients (ω_(i)(l)), and weighting means (311) for weighting saidfrequency components with said weighting coefficients.